1. CT8, April 2012 Question 5 requires expressing E(-X|X<-VaR_a) in the integral form which the answer states to be -1/a int_-inf^VaR_a XF(X) dx just wondering where does the 1/a part come from? 2. CM2B: for a general Brownian motion St¬lnN(lnS0+(mu-1/2 sigma^2)t ,sigma^2 t) can lnSt be simulated as norm.inv(rand(), mean, variance), where mean and variance are from the line above? Thank you
Question 1 Recall that P{A|B} = P{A, B} / P{B} = 1 / P{B} * P{A,B}. Here, B is X < -VaR_a, therefore 1 / P{B} = 1 / a. This is where the factor of 1/a comes from. Question 2 Yes.
